The Energy Cascade Rate in Supersonic Magnetohydrodynamic Turbulence

TL;DR

This study uses direct numerical simulations to analyze the energy cascade rate in compressible MHD turbulence, revealing how magnetic fields and Mach numbers influence energy transfer and the importance of increment calculation methods.

Contribution

It provides a detailed analysis of the energy cascade in compressible MHD turbulence across various regimes, highlighting the effects of anisotropy and increment methods on cascade rate estimates.

Findings

Cascade rates vary with sonic and Alfvénic Mach numbers.

Increment method choice affects flux and non-flux term contributions.

Strong magnetic fields induce anisotropic energy transfer.

Abstract

Three-dimensional direct numerical simulations (DNS) are implemented to investigate the energy cascade rate in compressible isothermal magnetohydrodynamic (MHD) turbulence. Utilizing an exact law derived from the K\'arm\'an-Howarth equation, we examine the contributions of flux and non-flux terms to the cascade rate across a broad range of sonic and Alfv\'enic Mach numbers, from subsonic to supersonic regimes and varying mean magnetic fields. Cascade rates are computed using on-grid 3-D decomposition and two plasma increment approaches: signed and absolute values. Anisotropy induced by strong magnetic fields is analyzed through angular-dependent scaling of the cascade terms. Moreover, the increment calculation method significantly influences the relative contributions of flux and non-flux terms, with absolute methods tending to overestimate the latter. These findings extend current studies of compressible turbulence and offer critical insights into energy transfer mechanisms relevant to many astrophysical phenomena.